Can yall please help me with this I really need help

Can Yall Please Help Me With This I Really Need Help

Answers

Answer 1

Answer:

i believe it is G

\( \frac{7}{3} \)


Related Questions

A person sitting in the top row of the bleachers at a sporting event drops a pair of sunglasses from a height of 24 feet. The function h=-16x^2+24 represents the height (h) (in feet) of the sunglasses after x seconds. How long does it take the sunglasses to hit the ground, rounded to the nearest tenth?

Answers

1.2 seconds  it take the sunglasses to hit the ground

To find how long it takes for the sunglasses to hit the ground, we need to find the value of x when h = 0.

We can set the function equal to 0 and solve for x:

-16x² + 24 = 0

Dividing both sides by -16 gives:

x² - (24/-16) = 0

x² - 1.5 = 0

x² = 1.5

x = ±√1.5

x = √1.5 seconds for the sunglasses to hit the ground.

we get x = 1.2 seconds.

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3(n-2)=9(6–n)
what is n ?

Answers

Answer:

n = 5

Step-by-step explanation:

Given

3( n - 2) = 9 ( 6 - n)

3n - 6 = 54 - 9n

3 n + 9n = 54 + 6

12n = 60

n = 60/ 12

n = 5

Answer:N=5

Step-by-step explanation:

3n-6=54-9n

+9n       +9n

12n-6=54

     +6  +6

12n=60

/12   /12

N=5

You have a mortagege of $275,000
after down payment with an interest
rate of 3% for 30 years.
What does P, r,n, and t are equal to?

You have a mortagege of $275,000after down payment with an interestrate of 3% for 30 years.What does

Answers

Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

the volume of water in a reservoir decreases 21,000 cubic yards over a 3-month period. what is the average change in volume per month?

Answers

The average change in volume per month when the volume of water in a reservoir decreases 21,000 cubic yards over a 3-month period is 7,000 cubic yards.

The question asks for the average change in volume per month when the volume of water in a reservoir decreases 21,000 cubic yards over a 3-month period. In order to calculate the average change in volume per month, we can divide the total change in volume by the number of months involved. This gives us an average rate of change per month. Therefore, to find the average change in volume per month when the volume of water in a reservoir decreases 21,000 cubic yards over a 3-month period, we can divide the total change in volume (21,000 cubic yards) by the number of months (3 months).21,000/3 = 7,000

Therefore, the average change in volume per month is 7,000 cubic yards.

The average change in volume per month when the volume of water in a reservoir decreases 21,000 cubic yards over a 3-month period is 7,000 cubic yards.

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Find the value of x in the ratio 2:8= 16:x​

Answers

Step-by-step explanation:

2/8 = 16/x

2x = 16×8

x = 16*8/2

x = 64.

Hope it helps :)

A recipe for a dozen iced cookies calls for 2 1/4 cups flour. Which can be used to determine the amount of flour needed to make 32 cookies?

Answers

Answer:

You can form a proportion to solve this problem.

Step-by-step explanation:

The proportion can look like this (there are other ways to write an equal proportion but this is just one of the ways you could go about it :)

\(\frac{2.25}{12}\)=\(\frac{x}{32}\)

12x=72

x=6 cups of flour

Hope this helps!! :)

Answer:

You can form a proportion to solve this problem.

Step-by-step explanation:

The proportion can look like this (there are other ways to write an equal proportion but this is just one of the ways you could go about it :)

=

12x=72

x=6 cups of flour

Which equation represents a line which is parallel to the line 7x - y = 4?

Which equation represents a line which is parallel to the line 7x - y = 4?

Answers

Answer:

Step-by-step explanation: step : Place the given line’s equation in slope- intercept form y = mx + b. A line parallel to this line will have the same slope.

7x - y = 4. Yields y = 7 x - 4. Therefore y = 7x - 5 is the correct answer.

Simplify the expression (10 + 3i)(10 − 3i).

I understand how to distribute and what not, i just don't know what to do with i.

I got to -9i^2+10

1st CORRECT answer gets brainiest .
i=i
i^2=-1
i^3=-i
i^4=1

Answers

Answer:

Step-by-step explanation:

91 − 60 i

Answer:

109

Step-by-step explanation:

is 20 bigger than -20

Answers

So imagine this the more right it is from zero the more greater it is ok so -20 is on the left so yes 20 is bigger than -29

Select the correct answer. What is the product (1 + i)(2 + i)? A. 3 + 2i B. 3 – i C. 3 + i D. 1 – 3i E. 1 + 3i

Answers

Answer:

1 + 3i

Step-by-step explanation:

1(2+i)+i(2+i)

1*2+1i+i(2+i)

1*2+1i+2+ii

2+i+2i-1

1+i+2i

1+3i

Multiplication is the process of multiplying. The product (1+i)(2+i) is (1+3i).

What is multiplication?

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The product (1+i)(2+i) can be done as,

(1+i)(2+i)

= 2 + i + 2i + i²

= 2+ 3i -1

= 1+3i

Hence, the product (1+i)(2+i) is (1+3i).

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A tv costs £800 plus VAT at 20%.
What is the total cost of the TV?​

Answers

Answer:

Step-by-step explanation:

800+20%

20%= (20/100)

800/100=8*20=160

add to original price= 800+160=960

Graph the function.
h(x) = -1/5x^2+2x

Answers

Answer:

Hello there I would love to assist but could you give me a little more info I think I know the answer but I want to make sure I got it 100% correct unless you cant give me more info ill just tell you what I think it is but if u can give me more info before I give u the answer to make sure its correct would be appreciated

Step-by-step explanation:

Kaitlin is making a circular vegetable garden for her service learning project. Her garden has a diameter of 30 feet. She wants to put up chicken wire around the outside of the garden so that animals don't eat the vegetables.
a) How many feet of chicken wire will she need? (Round your answer UP to the nearest foot)
b) If chicken wire costs $1.30 per foot, how much will she spend on chicken wire?​

Answers

The feet of chicken wire needed by Kaitlin would be 95 feet.

The total to be spent on chicken wire would be $ 123. 50.

How to find the feet and cost ?

The feet length would be the circumference of the circular vegetable garden which would be :

= π x diameter

The feet length is:

= π x 30

= 94. 25 feet

= 95 Feet

This then means that the cost of the chicken wire would be ;

= 95 x 1. 30 per foot

= $ 123. 50

In conclusion, the cost of the chicken wire would be $ 123. 50.

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can yall help me again plsssssssss!!!!!!!!!!!!!!!

can yall help me again plsssssssss!!!!!!!!!!!!!!!

Answers

After solving the given expression we get  a = b = 12 and q = r = 24.

What is fractiοn?

A fractiοn is a numerical quantity that represents a part οf a whοle οr a ratiο between twο quantities. It is written as a tοp number (numeratοr) οver a bοttοm number (denοminatοr), separated by a hοrizοntal line.

Tο subtract 2/3 - 1/4, we need tο find a cοmmοn denοminatοr fοr the twο fractiοns. The smallest cοmmοn denοminatοr is 12, sο we'll cοnvert each fractiοn tο an equivalent fractiοn with a denοminatοr οf 12:

2/3 = 8/12 (multiply bοth numeratοr and denοminatοr by 4)

1/4 = 3/12 (multiply bοth numeratοr and denοminatοr by 3)

Nοw we can subtract the twο fractiοns:

8/12 - 3/12 = 5/12

Sο 2/3 - 1/4 = 5/12.

Tο express the result as a fractiοn in the fοrm x/y, we can simply use the answer we fοund: x = 5, y = 12, sο:

2/3 - 1/4 = 5/12 = 5/12

Similarly, tο express the result as a fractiοn in the fοrm a/b, we need tο find anοther equivalent fractiοn with a cοmmοn denοminatοr. We can use 24 as a cοmmοn denοminatοr this time:

2/3 = 16/24 (multiply bοth numeratοr and denοminatοr by 8)

1/4 = 6/24 (multiply bοth numeratοr and denοminatοr by 6)

Nοw we can subtract the twο fractiοns:

16/24 - 6/24 = 10/24

Sο 2/3 - 1/4 = 10/24.

Tο express the result as a fractiοn in the fοrm a/b, we can simplify the fractiοn by dividing bοth numeratοr and denοminatοr by their greatest cοmmοn factοr, which is 2:

10/24 = (10 ÷ 2) / (24 ÷ 2) = 5/12

Sο we get a=b=12 and q=r=24.

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Find the distance between the given parallel planes. 3x - 4y + z = 12, 6x - 8y + 2z = 1

Answers

The distance between the given parallel planes is 11 / sqrt(26), or approximately 2.16 units.

To find the distance between the given parallel planes, we can use the formula for the distance between a point and a plane.

First, we need to find a point on one of the planes. We can choose any convenient point, such as setting z = 0. Let's set z = 0 in the first equation:

3x - 4y + 0 = 12

3x - 4y = 12

To make the calculations easier, let's rearrange this equation to solve for x:

3x = 4y + 12

x = (4y + 12)/3

Now we have a point in the form (x, y, z) on the first plane: ( (4y + 12)/3, y, 0 ).

Next, we can calculate the perpendicular distance from this point to the second plane. To do this, we'll use the formula:

distance = | ax + by + cz - d | / sqrt(a^2 + b^2 + c^2)

where (a, b, c) is the normal vector of the plane, and d is the constant term.

The normal vectors of both planes are the coefficients of x, y, and z in their respective equations.

For the first plane, the normal vector is (3, -4, 1).

For the second plane, the normal vector is (6, -8, 2).

The constant term for the second plane is 1.

Now we can substitute these values into the distance formula:

distance = | (3)((4y + 12)/3) + (-4)(y) + (1)(0) - 1 | / sqrt((3)^2 + (-4)^2 + (1)^2)

Simplifying:

distance = | 4y + 12 - 4y - 1 | / sqrt(9 + 16 + 1)

distance = | 11 | / sqrt(26)

distance = 11 / sqrt(26)

Therefore, the distance between the given parallel planes is 11 / sqrt(26), or approximately 2.16 units.

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The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.



Part A: Write a system of equations to represent the given scenario. Use the variables "s" for senior citizen tickets and "c" for child.



Part B: Solve the system of equations from Part A algebraically. Show your work.



Part C: Explain what the solution to the system of equations represents in context of the problem. Hint: You will need to put words here, not an equation.

Answers

Answer:

The school took in $52 on there second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen

Step-by-step explanation:

Given that a = (- 8) b = 2 c = 7 and d = 11 , solve for x, y, z, and w.
[[x + y, z], [z - x, w - y]] =
[[a, b], [c, d]]
What is the value of w?
(Only type a number, nothing else)

Answers

Answer:

24

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given: a = -8, b = 2, c = 7, d = 11

2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]

3) Matching up the elements in the matrices:

x + y = a = -8 (1)

z = b = 2 (2)

z - x = c = 7 (3)

w - y = d = 11 (4)

4) Solving the equations:

From (1): x + y = -8 => x = -8 - y

Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y

Substitute (2) into the above: 2 = 15 + y => y = 13

Substitute y = 13 into (1): -8 - 13 = -21 = x

Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24

Therefore, the values are:

x = -21

y = 13

z = 15

w = 24

So the final value of w is:

w = 24

What is the y-intercept of the line y + 6 = -4(X - 1.5)

Answers

Answer:

y=0.

y + 6 = -4(X - 1.5)

y+6 = -4x+6

y = mx+b

y=4x

There isn't a b, which is the y intercept, so the y int would be 0

the average house has 11 paintings on its walls. is the mean smaller for houses owned by teachers? the data show the results of a survey of 16 teachers who were asked how many paintings they have in their houses. assume that the distribution of the population is normal. use the classical approach.

Answers

The mean may or may not be smaller for houses owned by teachers. Further analysis is required to determine if the mean is indeed smaller for houses owned by teachers based on the given data.

In the survey of 16 teachers, the data collected on the number of paintings in their houses can be used to calculate the sample mean. By comparing this sample mean to the average number of paintings in houses in general (which is stated to be 11), we can assess if the mean is smaller for teachers' houses. However, it's important to note that the statement assumes a normal distribution of the population.

To determine if the mean is smaller, we would need to compare the sample mean of the teachers' houses to the population mean of 11. If the sample mean is statistically significantly smaller than 11, we can conclude that the mean is smaller for houses owned by teachers. This would require conducting appropriate hypothesis testing, such as a one-sample t-test, to assess the significance of the difference between the sample mean and the population mean.

Therefore, without further information or analysis, we cannot definitively determine if the mean is smaller for houses owned by teachers based solely on the statement that the average house has 11 paintings on its walls and the data from the survey of 16 teachers.

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Solve the inequality.

9p+23<41

Answers

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

p < 2

Answer:

p < 2

Step-by-step explanation:

9p + 23 < 41

9p < 18

p < 2

Image formation in a Pin-hole camera; Points, lines, and planes in 3D; Rotation and Stereo. A conventional pin-hole camera model is shown at the end. In this model, three points P,Q, and R, in the 3D scene are given to be: P(X1,Y1,Z1)=P(120,250,340)mm, corresponding image point: p(x,y) Q(X2,Y2,Z2)=Q(250,150,200)mm, corresponding image point: q(x,y) R(X3,Y3,Z3)=R(200,100,500)mm, and corresponding image point: r(x,y) and Focal length f=5 mm. Pixel size ps =0.010 mm. Image size =1000×1000 pixels. Image coordinate center is at the center pixel with indices (500,500). - 2+2 points) Stereo camera system (a) A second identical camera is placed with its lens center at C=(10,0,0). The coordinates axes of the two cameras are all paralle the pointing along the same directions (as in the case of a conventional parallel stereo camera system). Find the disparity (shift of its image position compared to the first camera) of the point P in the second camera. (b) The image coordinates of a point V is (x,y)=(1.0,2.0)mm in the first camera, and it is (1.5,2.0)mm in the second camera. What are the (X, Z,Z) coordinates of V in the 3D scene

Answers

In a pin-hole camera model, the three-dimensional (3D) points P, Q, and R in the scene correspond to their respective two-dimensional (2D) image points p, q, and r on the camera's image plane.

Given the coordinates of these points in the 3D scene and their corresponding image points, along with the focal length, pixel size, and image size, we can calculate various parameters. The image coordinate center is at the center pixel with indices (500,500).

For the stereo camera system, the second camera is placed parallel to the first one, with its lens center at C=(10,0,0) in the 3D scene. To find the disparity of point P in the second camera, we need to determine the difference in its image position compared to the first camera. Disparity is the horizontal shift between corresponding points in the two images. By calculating the difference in the x-coordinate of point P's image position in the two cameras, we can find the disparity.

To determine the 3D coordinates (X, Y, Z) of point V in the scene, given its image coordinates in both cameras, we can use triangulation. Triangulation involves finding the intersection point of two rays, each originating from the camera center and passing through the respective image point. By considering the known parameters of the cameras, we can compute the 3D coordinates of point V using its image coordinates in both cameras.

For the stereo camera system, the disparity of point P can be found by calculating the difference in its image position between the two cameras. To determine the 3D coordinates of point V, we can use triangulation by considering the image coordinates in both cameras along with the known camera parameters.

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Final answer:

The calculation of image disparity in the second camera and coordinates of a point in 3D scene involves concepts of geometry and trigonometry. The coordinates can be computed using formulas derived from rules of similar triangles.

Explanation:

The given question involves the operations of a pin-hole camera and a stereo camera system. The process of imaging and finding disparities in the cameras with different lens centers is a part of computer vision in Robotics. For the first part of the question where we need to find the disparity of a certain point P, Q, and R in the second camera, the disparity can be computed using geometry and trigonometry. It entails looking at how the image's position changes when moving from one camera to another.

For the second part, where we need to find the coordinates of a point V in 3D scene. The coordinates of point V can be obtained from the disparity between two locations of point V from the first and the second camera. Using similar triangles, we can compute the coordinates as:

X = Z * (x1 - x2) / (f * pixel size)

Y = Z * (y1 - y2) / (f * pixel size)

Z = f * Base line / ((x1 - x2) * pixel size)

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We wish to estimate the mean serum indirect bilirubin level of 4-day-old infants. The mean for a sample of 16 infants was found to be 5.98 mg/100cc. (a) What is the point estimate of the population mean for bilirubin level? (b) Assume the bilirubin levels in 4-day-old infants are approximately normally distributed with a standard deviation of 3.5 mg/100cc. Construct a 95 percent confidence interval for the population mean. State the probabilistic interpretation of the confidence interval. (c) Construct a 95% confidence interval for the population mean under the assumption that bilirubin levels in 4-day-old infants are approximately normally distributed, with mean for the sample of 16 infants was found to be 5.98 mg/100cc and standard deviation to be 2.9 mg/100cc. Compare the two confidence intervals.

Answers

a) The point estimate of the population mean for bilirubin level is 5.98 mg/100cc.

b) The 95 percent confidence interval for the population mean bilirubin level in 4-day-old infants is (4.27, 7.69) mg/100cc.

c) The 95 percent confidence interval for the population mean bilirubin level in 4-day-old infants, considering the updated standard deviation, is (4.56, 7.40) mg/100cc.

(a) The point estimate of the population mean for bilirubin level is 5.98 mg/100cc.

(b) To construct a 95 percent confidence interval for the population mean, we can use the formula.

Confidence Interval = point estimate ± (critical value) * (standard deviation / √(sample size))

The critical value for a 95 percent confidence interval is 1.96 (assuming a normal distribution). The standard deviation given is 3.5 mg/100cc, and the sample size is 16.

Confidence Interval = 5.98 ± (1.96) * (3.5 / √(16))

Calculating the values:

Confidence Interval = 5.98 ± 1.96 * 3.5 / 4

Confidence Interval = 5.98 ± 1.96 * 0.875

Confidence Interval = 5.98 ± 1.71

Confidence Interval = (4.27, 7.69)

The 95 percent confidence interval for the population mean bilirubin level in 4-day-old infants is (4.27, 7.69) mg/100cc.

The probabilistic interpretation of this confidence interval is that if we were to repeatedly sample 4-day-old infants from the population and calculate the confidence interval each time, approximately 95 percent of the intervals would contain the true population mean bilirubin level.

(c) Using the updated standard deviation of 2.9 mg/100cc from the sample of 16 infants, we can calculate the confidence interval again.

Confidence Interval = 5.98 ± 1.96 * (2.9 / √(16))

Confidence Interval = 5.98 ± 1.96 * 2.9 / 4

Confidence Interval = 5.98 ± 1.96 * 0.725

Confidence Interval = 5.98 ± 1.42

Confidence Interval = (4.56, 7.40)

The 95 percent confidence interval for the population mean bilirubin level in 4-day-old infants, considering the updated standard deviation, is (4.56, 7.40) mg/100cc.

Comparing the two confidence intervals, we can see that the second interval is slightly narrower than the first one. This is due to the smaller standard deviation used in the calculation, which results in a more precise estimate of the population mean.

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rob is asked to graph this system of equations: 6x + 2y = 5; y + 3x =2; how many times will the lines intersect? A. there is no way to tell without graphing the lines first. B. the lines will not intersect, cuz the system only has one system. C. the lines will intersect once. D. the lines will intersect more than once.

Answers

Answer:

  C

Step-by-step explanation:

A and B are wrong and with D they wouldn't be lines so imma go with C.

Sorry if it's wrong.

Solve for x: 5(x + 3) = 4(x - 3)
-18
-27
-3
-6
please help me im actually having a mental breakdown over this stuff​

Answers

Answer:

x=27

Step-by-step explanation:

It's gonna be okay! Just breathe!

You got this I believe in you!!

answer this if you know no links or ill report
5√5+6×∛5∞±√5

Answers

Answer:

52

Step-by-step explanation:

Answer:

idrk i'm just going to take ur points because my other account got banned for 24 hrs like bru.h ig :/

Step-by-step explanation:

What is the area of a triangle whose vertices are (4,0), (2,
3), (8,-6)?(using distance formula)
a) 2 sq. units b) 0 sq. units c) 1 sq. units d) 4 sq. units​

Answers

Answer:

The correct option is;

b) 0 sq, units

Step-by-step explanation:

The vertices of the triangle are;

(4, 0), (2, 3), (8, -6)

The distance formula fr finding the length of a segment is given as follows;

\(l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\)

Where, (x₁, y₁) and (x₂, y₂) are the coordinates of the end points of the line

For the points (4, 0) and (2, 3) , we have;

√((3 - 0)² + (2 -4)²) = √13

Distance from (4, 0) to (2, 3) = √13

For the points (4, 0) and (8, -6) , we have;

√((-6 - 0)² + (8 -4)²) = √13 =

Distance from (4, 0) to (8, -6) = 2·√13

For the points (2, 3) and (8, -6) , we have;

√((-6 - 3)² + (8 -2)²) = 3·√13 =

Distance from (2, 3) to (8, -6) = 3·√13

Therefore, the perimeter of the triangle = 6·√13

The semi perimeter s = 3·√13

The area of the triangle,  \(A = \sqrt{s\cdot \left (s-a \right )\cdot \left (s-b \right ) \cdot \left ( s-c \right )}\)

Where;

a, b, and c are the length of the sides of the triangle;

\(A = \sqrt{3\cdot \sqrt{3} \cdot \left (3\cdot \sqrt{3} -\sqrt{3} \right )\cdot \left (3\cdot \sqrt{3} -2 \cdot \sqrt{3} \right ) \cdot \left ( 3\cdot \sqrt{3} -3\cdot \sqrt{3} \right )} = 0\)

Therefore, the area = 0 sq, units.

Can y’all Hurry And Plzzz Help Me

Can yall Hurry And Plzzz Help Me

Answers

Answer:

C. its 7.5 per land

Step-by-step explanation:

Answer:

7.50 per lawn

Step-by-step explanation:

for two lawns it is 15 dollars and 15/2=7.50

so for 1 lawn it is 7.50

The graph below describes the journey of a train between two cities.
a) Work out the
acceleration, in km/h²,
in the first 15 mins
b) Work out the distance
between the two cities.
c) Work out the average
speed of the train during
the journey.

The graph below describes the journey of a train between two cities.a) Work out theacceleration, in km/h,in

Answers

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

According to the given question:

Each block of horizontal  is 1/8 hr = 7.5 min

Each block of vertical is 10 km/hr

Time                     Velocity  (km/hr)

0 Min  ( 0 hr)               0

15 Min (1/4 hr)           50

45 Min (3/4 hr)           50

60 MIn  ( 1 hr)           100

90 Min  ( 3/2 hr)        100

120 Min ( 2hr)             0

The acceleration in first 15 minutes = (1/4 hr)  =  (50 - 0)/(1/4 - 0)  = 50/(1/4)

= 200  km/h²

The distance between the two cities =

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

Distance between two cities = 125 km

Average Speed of train during the journey = 125/2  = 62.5  km/hr

Therefore,

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

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compare these amounts. use or =.

8oz ________ 8 cups

Answers

Answer:

8 cups is greater then 8 oz

Step-by-step explanation:

The 3 lines x = 3, y – 2. 5 =-(x – 0. 5), and y – 2,5 = x – 3. 5 intersect at point P.

Find the coordinates of P. Verify algebraically that the lines all intersect at P.

Answers

All three equations are satisfied when x = 3 and y = 2, which means that the lines intersect at the point (3, 2).

To find the coordinates of point P where the three lines intersect, we need to solve the system of equations formed by the three lines:

x = 3 (equation 1)

y - 2.5 = -(x - 0.5) (equation 2)

y - 2.5 = x - 3.5 (equation 3)

From equation 1, we know that x = 3. substituting this into equations 2 and 3, we get:

y - 2.5 = -2.5 (from equation 2)

y - 2.5 = -0.5 (from equation 3)

Simplifying these equations, we get:

y = 0 (from equation 2)

y = 2 (from equation 3)

So the coordinates of point P are (3, 2).

To verify that the lines all intersect at this point, we can substitute these coordinates into each of the original equations and check that they hold:

For equation 1: x = 3 holds when x = 3.

For equation 2: y - 2.5 = -(x - 0.5) becomes y - 2.5 = -(3 - 0.5) = -2 holds when x = 3 and y = 2.

For equation 3: y - 2.5 = x - 3.5 becomes y - 2.5 = 3 - 3.5 = -0.5 holds when x = 3 and y = 2.

So all three equations are satisfied when x = 3 and y = 2, which means that the lines intersect at the point (3, 2).

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